1. Field of the Invention
The present invention relates generally to digital signal processing and, more particularly, to the demodulation of a body angular-rate signal for use in a navigation and flight-control system.
2. Description of Related Art
Information often modulates an underlying carrier signal, thereby producing a modulated information signal. This same carrier signal is required, with a few modifications, to demodulate the modulated information signal. This required signal is called the demodulation-reference signal. It must be complex, that is, it must contain separate in-phase and quadrature outputs. A degraded version of this signal is often available with the correct frequency, but with the wrong phase and amplitude, and with a zero frequency or direct-current offset.
The source of the modulated information signal may be, for example, a quartz angular rate sensor. The degraded demodulation-reference signal may come from the apparatus driving the source of the modulated information signal, or it may come from the source of the modulated information signal itself.
A sensor incorporating a resonator can be driven with a known periodic drive signal. The drive signal preferably has a frequency at or close to the natural frequency of the resonator, and preferably has a shape which is a sinusoid with constant amplitude. Other frequencies and shapes can be used depending on the application, but such alternative applications will be very rare. The resonator responds to the drive signal by producing a data output signal which is a quadrature amplitude modulated (QAM) double-sideband suppressed-carrier (DSBSC) modulation of the drive signal. The output signal depends on the drive signal, and further depends on the parameters of the resonator, but these are known. Over short periods of time, they may productively be considered to be fixed.
One type of sensor system comprises an inertial-measuring unit (IMU) known as the Digital Quartz IMU (DQI). The sensed information of the DQI is the angular rate of rotation, but other resonators could just as easily be designed to respond to information about any of a number of other sensed parameters: temperature, viscosity, or anything else. The sensed information which is desired to be extracted has amplitude-modulated the drive signal cos(xcfx89dt); that should be the sensor output signal, y(t)=x(t)cos(xcfx89dt), where x(t) is the sensor input signal (a direct indication of angular rate, viscosity, etc.) and xcfx89d is the drive frequency. In order to extract the sensed information one could therefore (ideally) demodulate the sensor output signal using the drive signal as the reference.
There are some flaws with this reasoning. The sensor output signal is actually expressed as:
y(t)=[x(t)+A]cos(xcfx89dt+xcfx86)+B sin(xcfx89dt+xcfx86)xe2x80x83xe2x80x83Equation 1
The variables A, B and f can drift with temperature and aging. The demodulation of the resonator data output signal is complex. That is, the resonator data output signal is separately multiplied by two periodic signals (generally sinusoids) which are known to be in quadrature. The first is referred to as the in-phase reference signal, and the second is referred to as the quadrature-phase reference signal. This multiplication thereby produces an in-phase product signal and a quadrature-phase product signal.
A set of three solid-state gyroscopes known as quartz rate sensors (QRS), plus a set of three solid-state accelerometers, plus all of their associated support and signal-processing electronics are packaged into a compact rugged mechanical assembly with the necessary vibration isolators and environmental controls to comprise the DQI. The DQI provides 3-axis body angular-rate information and 3-axis acceleration information for a full 6-degree-of-freedom (6-DOF) output. The 6-DOF output is available at a 600 sample/second/sensor data rate over a standard AMRAAM interface. The 6-DOF data outputs are used as inputs directly to autopilot/flight-stabilization controllers, and as inputs (alone or augmented by sensors such as GPS receivers) to a navigation computer.
The outputs of each QRS instrument are subject to undesirable phase shifts, which can vary with time and between the various QRS instruments. For proper operation, the demodulation reference signal must be phase shifted back an equal and opposite amount within the demodulator. One prior-art demodulator requires the use of two QRS-instrument-specific calibration numbers. The demodulator has several (usually three) stages where the gain of each stage is a function of the demodulation-reference frequency (which reference frequency is different for each instrument). The demodulator performs a gain correction using the downloaded calibration inputs. Similarly, the demodulator corrects the instrument-physics-caused phase-shift error in the demodulation-reference signal (which phase-shift error is again different for each instrument) using downloaded calibration inputs. These corrections are necessary for the proper and accurate operation of the DQI. Unfortunately, there are three possible problems that arise from using these calibration and correction procedures. First, the calibration inputs may be in error because QRS instrument parameters change with time and environmental influences; second, there may be factory errors in measurement and/or recording the calibration data; third, there may be human error in physically connecting the instrument to the correct memory which contains the calibration data.
The phase-shift-error problem can be substantially eliminated by combining with the demodulator an automatic phase-shift corrector; specifically, Applicant""s invention disclosed in U.S. Pat. No. 5,764,705, xe2x80x9cAdaptive Phase-Shift Adjuster for Resonator.xe2x80x9d This automatic phase-shift corrector, however, requires that the frequency-sensitive gains be corrected, just as with the rest of the demodulator. Such sensitivities may be substantially eliminated at the cost of additional computation, but more importantly, at the cost of greater delays in the demodulator. Because the I-channel output is in the feedback flight-control loop, any unnecessary delay is intolerable.
One particular recurrent problem relates to automatic amplitude normalization of a sinusoidal signal of fixed amplitude at the output of a digital elemental Hilbert transformer (EHT) as the nominal 10 kHz demodulation-reference frequency wanders with time and/or environmental influences such as temperature. Conventional wisdom and Hilbert-transformer design would lead one to widen the bandwidth of the Hilbert transformer, such as is done routinely in the design of applications such as communications systems. The problem is that as the bandwidth of the Hilbert transformer is increased, the delay times increase. Although this may be no problem for a communications application, it is fatally intolerable for a feedback-control system.
The invention which is the subject of this application provides a means to eliminate the frequency-sensitive gains in the demodulator without increasing the delays. A minimum-delay structure is maintained with the inventive capability of automatically correcting its gain in response to changes in the signal frequency.
A Hilbert transformer input is a sinusoidal signal, xn, whose frequency lies within a specified range. The input frequency is assumed to be fixed and under sinusoidal steady-state conditions, or very slowly time varying. The amplitude of the sinusoidal signal, yn=Kn(xnxe2x88x92xnxe2x88x922) at the output of the Hilbert transformer is dynamically set to match the amplitude of the input by adjusting the value of Kn as described in the paragraph below. For fixed gain Kn=K, the z transform of the relationship between xn and yn is
Y(z)/X(z)=K(1xe2x88x92zxe2x88x922)=zxe2x88x921j[2K(zxe2x88x92zxe2x88x921)/(2j)]xe2x80x83xe2x80x83Equation 2
The term zxe2x88x921 denotes a single sample period of pure delay. The heart of the Hilbert-transform operation is j=SQRT(xe2x88x921). In order for this operator to have a unit gain in response to a sinusoidal steady-state signal of frequency xcfx89d the present invention sets z=exp(jxcfx89dT) and finds that the gain must be K=1/[2 sin(xcfx89dT)]. Since K must be free to chase after its optimum value in accordance with the present invention, the fixed K is replaced by a time varying Kn, the value of the gain at sample time n. In order to generate a simple-to-mechanize, functionally robust error signal, en, a second Hilbert transformer is employed in tandem with the first. For convenience an equation un=ynxe2x88x92ynxe2x88x922 is defined, so that the output of the second Hilbert transformer is wn=unKn, which, for proper Kn, is wn=xe2x88x92xnxe2x88x922. The simple gain-sensitive error is defined to be en=xnxe2x88x922+wn.
The value of Kn is adaptively computed using the well known least mean squared (LMS) criterion. The unbiased instantaneous estimate of the mean-squared error is en2. The steep-descent parameter-adjustment algorithm calls for setting the rate of adjustment of Kn proportional to the negative of the gradient of en2, or to xe2x88x92xcexcengn, where the error gradient is gn=yn+un, and xcexc is a constant that governs the convergence rate. The xcexcengn product is integrated (or accumulated), and finally scaled and biased (to match the specified frequency range) in order to maximize the usable dynamic range of the accumulator. That scaled and biased output is Kn. This demodulator has three Hilbert transformer units in the direct signal-processing path, plus a fourth one used in the generation of Kn, all of which are driven directly by Kn.
Although the present invention is particularly well suited to the above-mentioned quartz angular rate sensor, it is well suited to any application in which there is an amplitude-modulated information signal, and in which there is a degraded demodulation-reference signal which must be upgraded enough to demodulate the amplitude-modulated information signal.
The present invention, together with additional features and advantages thereof, may best be understood by reference to the following description taken in connection with the accompanying illustrative drawings.